Persistence of Images on the Retina--The Use of Coloured Discs.
Fig. 39.--Disc to cause alternate opening and closing of two Slits.
By this time we must be thoroughly convinced that by throwing one
coloured patch over another a compound colour can be formed; our next
business is to demonstrate that the same effect can be produced by
successive images of these same colours. Thus we can show that as a
mixture of red and blue produces purple, when the two lights are
superposed, so precisely the same purple can be produced by allowing the
same two colours to strike the eye alternately, and in very rapid
succession. We can make a match of the beautiful purple of permanganate
of potash as before upon the screen, by placing one adjustable slit in
the red and the other in the violet. If we place in front of the slits a
disc cut out with equal angular apertures (Fig. 39), the slit S1 will be
covered when the slit S2 is open, and _vice versâ_, and the two will
never be uncovered at the same time when the card is turning round its
centre. When this disc is caused to rotate rapidly, we shall have first
a patch formed by the light coming through one slit, and then another
formed by that coming through the other slit, thrown on the screen on
the same place in rapid succession, and the effect on the eye should be
precisely the same as if the disc was not there, save in the matter of
intensity. Applying this artifice experimentally to the two slits which
were used to give the colour of permanganate, the experiment tells us
that such is the case. It would be going away from the intention of
this work were the physiological aspect of this experiment dwelt upon;
it need only be stated that an impression on the retina lasts an
appreciable time, though short, and that the impression made by the blue
patch has not had time to disappear before there is an impression made
by the red patch, and so on. As the retina retains these two impressions
together, they produce the impression of purple.
Fig. 40.--Disc painted Blue and Red.
For experiments in colour this duration of impressions is of great
value, for we can take advantage of it to compound the colours of
pigments together in a very simple manner. For instance, we can take a
circular disc painted in sectors with blue and red (Fig. 40), and
produce a purple by causing it to rotate round its centre. Small discs
of two inches in diameter may be painted with different coloured
sectors, and if a pin be passed through the centre, a smart movement of
a finger at the periphery will cause it to rotate sufficiently quickly
to make the colours blend. A more convenient plan for exact work is,
however, to have an electro-motor similar to that which moves the
rotating movable sectors (Fig. 41), and at the end of the spindle to fix
a cap with a screw and nut attached. The disc, perforated at the centre
with a clean-cut hole, can be slipt over the screw, and fastened by the
circular nut. When the armature rotates, the disc also rotates at the
same speed, and the colours thus blend without any exertion on the part
of the observer. Ordinary tops can also be used, but it is somewhat
fatiguing to have to wind them up and start them afresh for each
experiment. The motor shown in the figure rotates sufficiently rapidly,
with discs of eight inches in diameter, to blend colours. It may here be
remarked that the stronger the light in which such sectors rotate, the
quicker the rotation should be. Too slow a rotation allows a
scintillation which is destructive of accuracy of reading. To blend some
colours together also requires more rapid rotation than with others. The
brighter the colour the more rapid it should be. We learn from this that
the diminution of the more intense impressions on the retina is more
rapid at first than of the feebler.
Fig. 41.--Electro-motor with Discs attached.
Fig. 42.--Method of cutting Disc to allow an overlap of a second Disc.
Very convenient discs for producing colours by rotation of sectors may
be made by the following: vermilion (V), emerald green (E), French
ultramarine blue (U), chrome yellow (Y), lamp-black (X), and (zinc)
white (W). With these nearly every colour can be produced, or its value
derived. The chrome yellow disc is somewhat superfluous, but is
sometimes useful. The alteration in the proportions of the colours can
be readily made by Clark-Maxwell's plan. From the circumference to the
centre he cut the discs open, as at _ab_ (Fig. 42). Any moderate number
of discs, similarly cut, may be slipt over one another, and only a
sector of each is left visible. It should be remarked that this
necessitates the rotating apparatus being viewed with a direct light, as
in the case of two or three overlapping discs it is impossible to keep
them entirely flat, and shades are apt to be introduced. If we wish to
produce a white, or rather a grey, from three colours, we can take three
small discs of V, E and U, of equal diameter, and behind them place
discs of black and white, of larger diameter, rotating the whole five on
a common centre. We shall find that by altering the proportions of the
three first we can get a grey which can be exactly matched by a mixture
of black and white, X and W. It has already been shown that even
lamp-black reflects a certain amount of white light, so this amount of
reflected white light has to be added to the white in the outside
sectors. In the sectors used in the following experiments it was found
that the following proportions of the three colours were required--
V = 124°
E = 143°
U = 93°
----
360°
and to make the same grey it required
X = 278°
W = 82°
----
360°
Now the black reflected 3·4% of white light, so that really the
proportions of black and white were
X = 268·6
W = 91·4
-----
360·0
These matches were made in the light emitted by the crater of the
positive pole of the electric light, and are correct only for this
light. The greys here are dark greys, and such greys can be matched
exactly by throwing the white light in which the comparisons were made
on a white card, and reducing the intensity by means of the rotating
sectors. We can prove whether our matches are fairly correct from our
previous measures of the luminosity of these three colours, in
comparison with that of white. The luminosities of V, E, and U, as
found from the measures (pp. 93-95), are 36, 30, and 4·4, white being
100; 124 of V would have a luminosity of (124x36)/360, or 12·4; 143 of E
would have 11·92; and 93 of U would have 1·14; which, added to either,
give a luminosity of 25·46. The luminosity of 91·4/360 of white, which
is that of the mixture of black and white, comes to 25·39, so that we
may assume our observations have been fairly correct.
The influence of the kind of light in which the match was made is well
exemplified by taking the matched discs whilst rotating into a room
illuminated by the light from the sky, when it is seen that the grey of
the outer discs is bluish; or again, if the matched discs be examined in
gaslight, the inner grey will be found too blue.
The match of grey in this last light was found to be
V = 119°
E = 148°
U = 93°
----
360°
which matched with
X = 244°
W = 116°
(In this case the black and white are the corrected black and white.)
The importance of making matches in a uniform light is fairly
demonstrated by this experiment, and we cannot be wrong in asserting
that as skylight and sunlight and cloudlight (the last being often a
mixture of the two first), are so variable no measures made on one day
can be fairly compared with those made on another, more especially if
the observers are different. With an emerald green, a vermilion, an
ultramarine, a white, and a black disc any colour may be reproduced in
the rotation apparatus, the three first nearly matching what we have
already stated to be the three primary colours.
It may seem curious that both black and white may have to be mixed with
the colours, to produce a pigment colour; but a little reflection will
show how it is. For instance, suppose we want to know the colour
composition of gamboge (Y) in terms of vermilion (V), emerald green (E),
and ultramarine blue (U). We must make a disc painted with gamboge, and
also a black and a white disc of the same diameter, but rather larger
than the other three discs, and place them on the spindle of the
electro-motor (Fig. 43). We shall soon see on rotating them that no blue
is required in the inner disc, and that all that remains to do is to use
the red and the green. Mix these two, however, in whatever proportions
we may, the mixture will never attain the same luminosity, consequently
we must darken the yellow with black. Even then we shall find that, add
what black we may, the rotating red and green sectors will always be a
little less saturated with colour; which means that on rotation they
produce a certain quantity of white light mixed with the yellow. This we
might expect, for as emerald green, besides green and red, also contains
a fair proportion of blue, and as red, green and blue when mixed give
white, it follows that when V and E are rotated together, a grey or
subdued white light must be mixed with the colour produced. Turning back
to Chapter XIII. we also see that as the emerald green is expressible by
a single ray of the spectrum, mixed with white light this result might
have been foretold.
Fig. 43.--Arrangement to find value of Gamboge in terms of Emerald Green
and Vermilion.
This necessitates adding some white to the rotating sectors of the
yellow and black, as the yellow reflects but little white light, and
finally we shall get an absolute match, of which the final results are
172 V + 188 E = 75 Y + 45 W + 240 X.
This equation is full of meaning. It tells us in the first place what we
have already known, that V and E are one or both impure colours, and
that when rotated together in the proportions indicated, they produce at
least a luminosity of white equal to 53/360 of a white disc (as the
black used reflected just 3·4% of white light). Further, it tells us
that we can obtain the luminosity of Y, when we know the luminosities of
V and E. At page 186, the luminosities of these colours are given as 36
and 30 respectively, white being 100. This makes the luminosity of the
colours on the left hand of the equation 17·2 + 15·67, or 32·87, and on
the right =75/360= Y + 14·76, and consequently the luminosity of Y =
86·9. In the same way we can obtain any other colour in terms of these
standards.
We may here show how we can obtain the luminosity of any colour by means
of the three inner discs, and the black and white outer discs. We have
already shown that any colour may be matched by the combination of not
more than two simple colours, after deducting white from it; and from
this we deduce that any coloured pigment will form a grey with some two
of the three coloured discs, V, E, and U; and this being done we can
then calculate the luminosity. For instance, with an orange-coloured
pigment we should proceed to make a disc of the same diameter as that of
the three above; an inspection would show us that in this colour red
predominates, and therefore we could do without the red disc. We should
then alter the proportions of V, U, and O, till they gave a match which
was the same as that of a grey given by the rotating black and white
sectors.
In an experiment with an orange of this kind, the following results were
obtained--
E 115° }
U 150° } = { W 85°
O 95° } { X 275°
We can now from these deduce the luminosity of the orange employed in
this case.
The luminosities of E and U, as already found, were 30 and 4·4, whilst
the black (X) reflected 3·4% of white light; we thus get the following
equations--
115 x 30 + 150 x 4·4 + 95 O = (85 + 3·4 x 275) 100.
This gives 95 O = 9435 - (3450 + 660).
O = 56.
That is, the luminosity of the orange is ·56 that of white; by direct
measurement it was ·57.
In a similar way the luminosity of chrome yellow (Y) is found. In this
case--
E 35 }
U 204 } = { W 101
Y 121 } { X 259
Similar equations were formed as the above.
35 x 30 + 204 x 4·4 + 121 Y = (101 + 3·4 x 259) 100
whence Y = 77·6.
That is, the luminosity of the chrome yellow is ·78; the same as was
obtained by direct measurement.
In the same manner the luminosity of any colour can be found. Thus that
of a purple, or of green, can be ascertained; of the former by using the
green disc with either the red or the blue disc, and the latter by the
red and blue disc. From this it is apparent that we can check the
luminosities derived from other means by this plan.
A taking experiment can be made with colour discs to imitate all the
colours of the spectrum in their proper order, though diluted more or
less by white light. This can be done by rotating V, E, and U together;
but in order to get additional luminosity in the yellow, we can use
chrome yellow as well. If a disc be made as in the figure (Fig. 44), it
will on rotating give a fair imitation of the spectrum, if it be viewed
through a slit held in front of the disc.
Fig. 44.--Disc arranged to give approximately all the Spectrum Colours.
The mixture of colours by means of rotating sectors is one which the
artist cannot use for artistic purposes, and it might seem that for him
any deductions made from this method are useless; but it is not so.
Suppose we take black lines ruled closely together on paper, and examine
the surface from such a distance that the lines are no longer
distinguishable it will appear of a grey; and if we take the amount of
black on the paper and amount of white, and prepare two sectors of black
and white, whose angles are in these proportions, and rotate them
alongside the ruled surface, it will be found that the grey of one
matches the grey of the other. If instead of lines of black and white we
have them of light yellow and cobalt blue, a grey is also produced when
the surface covered by the blue is to that covered by the yellow in
correct proportions, and may be matched by rotating sectors containing
merely black and white. Now some artists employ stippling, filling up
cross-hatching of one colour with dots of a totally different colour, or
they place dots side by side. When seen from the distance at which the
picture should be viewed, these various colours blend one into another,
and form a tint which is the same as that which would be obtained by
rotating these colours together in the proportion in which they cover
the ground. Artists, however, generally mix their pigments together on
the palette, and the resulting mixtures are often totally unlike those
which are obtained by rotating the same colours together, a noteworthy
example is that of yellow and blue. By rotation, and when in proper
proportion, these two give a white, but when mixed on the palette a
green results. What causes this difference? Experimental proof is always
the most satisfactory proof, so let us have recourse to the spectrum
apparatus to obtain an answer. Let a spectrum be thrown on the screen,
and in it place a strip of paper painted with the yellow, and then
another with the blue. With the first it will be seen that the blue rays
are not reflected, but only the green and yellow and red, taking the
spectrum as roughly made up of these four colours. With the latter the
yellow is not reflected, and but very little red, but the blue and the
green are reflected strongly. Now we have already said that the
reflection of colour from a surface is indicative of the colours the
particles of pigments when taken thin enough to be transparent would
transmit; hence we may take it that the yellow pigment transmits the
red, yellow, and green, and the blue pigment scarcely anything but blue
and green. When we have a mixture of these fine particles of pigment on
paper, some will underlie the others. But let us pay attention to what
would happen if a yellow particle were at the top, and a blue one
beneath it. White light would impinge on the yellow particle, but only
red, yellow, and green would pass out or be reflected from it. This
sifted light would next fall on the blue particle and--as we have
seen--only blue and green can pass through or be reflected from it; but
as the yellow particle has already deprived the white light of its blue
component, the green light alone would pass to the paper, and be
reflected either direct from the surface of the paper, or through the
particles themselves to the eye. If the blue particle were on the top,
precisely the same effect would be produced; it would only allow blue
and green to pass to the yellow particle, and as the yellow is opaque to
the blue, only green light again would pass. Similarly if side by side
the same phenomena would occur, since the light reflected from one on to
the other would be deprived of all colour except the green. A very
pretty experimental proof of this is to place a yellow solution of dye
in front of the slit of the colour apparatus, and having formed the
yellow colour patch to place in it a piece of paper covered with a blue
pigment: the latter becomes green. By placing a blue solution in front
of the slit, and using a piece of yellow pigmented paper, the same
result is obtained. The artist therefore in mixing his pigments calls
into play the law of absorption, and from his mixtures very naturally
assumes that blue and yellow make green. He makes a neutral tint of
blue, red, and yellow, and as the red cuts off the green, this naturally
follows from the above. Such experiments as these led him to the
conclusion that red, yellow, and blue are the three primary colours, an
assumption which had he used simple spectrum colours instead of compound
colours, such as pigments, he would not have ventured to make.